add research proposal/plan

- plan.tex: add submitted proposal.
- plan.pdf: generated pdf file.
- sources.bib: merged sources for plan.tex.
- .gitignore: add .aux/ directory with latex stuff

Signed-off-by: Aiden Woodruff <woodra@rpi.edu>

4 files changed, 185 insertions, 0 deletions

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..837db7b
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+# LaTeX auxiliary files
+.aux/
diff --git a/plan.pdf b/plan.pdf
new file mode 100644
index 0000000..9dde119
--- /dev/null
+++ b/plan.pdf
diff --git a/plan.tex b/plan.tex
new file mode 100644
index 0000000..766e6ad
--- /dev/null
+++ b/plan.tex
@@ -0,0 +1,139 @@
+\documentclass{article}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+
+\usepackage[backend=biber]{biblatex}
+\addbibresource{sources.bib}
+
+\title{FNS25 Research Plan}
+\author{Aiden Woodruff}
+
+\begin{document}
+\maketitle
+
+\section{Selected paper}
+
+The selected paper is ``Experimental evidence for tipping points in social
+convention'' by Centola et al. \cite{centola_experimental_2018}. The social
+science report is cited across disciplines from swarm robotics to virology.
+
+\subsection{Main topic}
+
+Centola et al. collect experimental evidence to support theoretical models of
+tipping points in social conventions. The prior work on critical mass as
+defined in game theory and observational studies suggest dedicated minorities
+of anywhere from 10-40\% of a population are large enough to effect changes in
+conventions. The authors vary the size of minority groups to determine the
+threshold past which dedicated actors are able to disrupt the convention in
+a name game.
+
+\subsection{Methods}
+
+The study engaged 194 online subjects in a game where pairs of players
+coordinate in naming a picture of a person for their own gain. Participants
+were randomly assigned to independent groups of variable size. Within those
+groups, members were matched pairwise for a number of rounds. Each round, pairs
+of players interacted each round to gain 10\textcent{} if their names matched
+or else lose 10\textcent.
+
+When a naming convention was reached, dedicated confederates were introduced
+which simultaneously chose the same alternative (chosen from common previous
+played names). The theoretical tipping point was 25\% of the population, and so
+committed minorities in the range of 15\% to 35\% were introduced across
+different trials.
+
+Centola et al then developed a model based on a simple sliding window of memory
+which was able to predict 80\% of experimental results. They used the model to
+increase population size further and find a more exact critical mass
+percentage.
+
+The model was implemented in R and provided as part of supplementary materials
+on GitHub.
+
+\subsection{Data}
+
+The details of each round were recorded, including: group sizes, round counts,
+all names assigned by players in each round, and confederate sizes and
+behaviors. Experimental data were used to tune the sliding window memory model.
+Then minority and group sizes, memory, network density, and strategy preference
+were varied to achieve more accurate values for the tipping point.
+
+\subsection{Results and conclusions}
+
+The tipping point was found to be around 25-31\% of the population empirically
+and more precisely around 24.3\% for the developed model. The results of
+Centola et al. align well with certain qualitative studies in organizational
+settings, which they suggest may be due to the rewards of following convention
+being clearly defined. When they adjusted agent strategy preferences, the
+tipping point remained below 50\%.
+
+They extend their discussion to understanding intentional pushes to change
+social opinion and naturally evolving acceptability of different social
+behaviors.
+
+Centola et al. provided an emperical value for tipping points which is widely
+cited. Their work also supports the idea that the tipping point is precise in
+a population \cite{babitz_how_2025}.
+
+\subsection{Evaluation}
+
+Centola et al. build on similar games and their disciplines own conventions to
+devise this study. Their results are not general to every social convention but
+still serve as empirical evidence for the critical mass phenomenon. The
+proposed model provides a method to explore other hypotheses. The raw data can
+also be used to develop and test other models. Since their own sliding window
+memory model only predicted 80\% of experimental subject choices (even with
+longer memories), there may well be a better model which can be tuned to their
+data.
+
+Even without the more precise threshold predicted by Centola et al.'s model,
+their experimental threshold is a nice result.
+
+\section{Experimental proposal}
+
+\subsection{Goal and novelty}
+
+My goal is to replicate the sliding window memory model used by Centola et al.
+and vary the strategy preference among certain members of the network. I am
+hoping to more accurately model real world networks in which certain actors
+have much a greater aversion to changing conventions than others. Additionally,
+I want to try specifically adjusting the influence (i.e. node degree) of those
+individuals.
+
+\subsection{Data}
+
+I plan to run experiments on actor networks of the same type as Centola et al.
+I will choose different independent variables and determine tipping points for
+each configuration.
+
+I will also explore for data from similar studies to compare my results to.
+
+\subsection{Methods}
+
+I plan to use SNAP \cite{leskovec2016snap} for network infrastructure and
+analysis. The code implemented by Centola et al. is written in R and seems to
+run slowly on my machine. The code is short (less than 200 lines overall) and
+so I plan to re-implement it in C++.
+
+The tipping points found by Centola et al. were robust to network density, so I
+will plan to study less dense networks. Depending on the trial, I will
+introduce influential nodes of high degree.
+
+Smaller network were more susceptible to dedicated minorities, and so I am also
+interested in how variable strategy preference will affect small networks like
+those in the experiments (\(\le 30\) participants).
+
+Additionally, if I have time I may try to construct a different model that can
+more accurately predict the experimental data from Centola et al. Then it will
+be worth repeating the same experiments to see how the results differ.
+
+\subsection{Result evaluation criteria}
+
+Statistical significance will be a necessary result for a successful study. My
+hypothesis is that influential conservative nodes will cause the tipping point
+to be higher in small networks but not as much in large networks.
+
+\printbibliography
+
+\end{document}
+
diff --git a/sources.bib b/sources.bib
new file mode 100644
index 0000000..274d19b
--- /dev/null
+++ b/sources.bib
@@ -0,0 +1,44 @@
+@article{centola_experimental_2018,
+        title = {Experimental evidence for tipping points in social convention},
+        volume = {360},
+        url = {https://www.science.org/doi/full/10.1126/science.aas8827},
+        doi = {10.1126/science.aas8827},
+        abstract = {Theoretical models of critical mass have shown how minority groups can initiate social change dynamics in the emergence of new social conventions. Here, we study an artificial system of social conventions in which human subjects interact to establish a new coordination equilibrium. The findings provide direct empirical demonstration of the existence of a tipping point in the dynamics of changing social conventions. When minority groups reached the critical mass—that is, the critical group size for initiating social change—they were consistently able to overturn the established behavior. The size of the required critical mass is expected to vary based on theoretically identifiable features of a social setting. Our results show that the theoretically predicted dynamics of critical mass do in fact emerge as expected within an empirical system of social coordination.},
+        pages = {1116--1119},
+        number = {6393},
+        journaltitle = {Science},
+        author = {Centola, Damon and Becker, Joshua and Brackbill, Devon and Baronchelli, Andrea},
+        urldate = {2025-09-09},
+        date = {2018-06-08},
+        note = {Publisher: American Association for the Advancement of Science},
+        keywords = {read},
+        file = {Full Text PDF:/Users/aiden/Zotero/storage/WXKTX67T/Centola et al. - 2018 - Experimental evidence for tipping points in social convention.pdf:application/pdf},
+}
+
+@article{leskovec2016snap,
+  title={SNAP: A General-Purpose Network Analysis and Graph-Mining Library},
+  author={Leskovec, Jure and Sosi{\v{c}}, Rok},
+  journal={ACM Transactions on Intelligent Systems and Technology (TIST)},
+  volume={8},
+  number={1},
+  pages={1},
+  year={2016},
+  publisher={ACM}
+}
+
+@article{babitz_how_2025,
+        title = {How social norms emerge: The interindividual actor–critic.},
+        issn = {1939-1471},
+        url = {https://research.ebsco.com/linkprocessor/plink?id=207f0ced-fbf3-32e9-8d22-d35b55e623b3},
+        doi = {10.1037/rev0000585},
+        shorttitle = {How social norms emerge},
+        abstract = {Social norms shape a vast range of human behaviors, from everyday interactions to major life choices. Yet, existing theories of norm emergence typically focus either on why certain norms arise (substantive properties) or on how they spread and persist (dynamical properties), often making conflicting assumptions. Here, we propose a unified account in which norms prescribing how one ought to act emerge naturally from the fundamental algorithms that guide learning—whether in social or nonsocial settings. Our account builds on recent advances in decision making and emotion research that have highlighted “actor–critic” models as a core mechanism of learning from feedback. We extend this mechanism to social settings by assuming that it is not only we who critique our actions; others critique our actions as well. By simulating this interindividual form of learning, we show that it uniquely produces group behavior that exhibits both substantive and dynamical properties of real-world social norms, including prosociality, ingroup bias, stickiness, S-shaped curves, and local conformity/global diversity. Our framework thus offers a uniquely parsimonious way to bridge the gap between individual learning and group behavior. ({PsycInfo} Database Record (c) 2025 {APA}, all rights reserved)},
+        journaltitle = {Psychological Review},
+        shortjournal = {Psychological Review},
+        author = {Babitz, Danielle and Eldar, Eran},
+        urldate = {2025-10-15},
+        date = {2025-09-29},
+        note = {Publisher: American Psychological Association},
+        keywords = {Learning, Reinforcement, Social Cognition, Social Norms},
+        file = {Full text PDF:/Users/aiden/Zotero/storage/APF8VC8A/Babitz and Eldar - 2025 - How social norms emerge The interindividual actor–critic..pdf:application/pdf},
+}